There's a war over Damian Lillard ... with several "major" record labels vying to sign the NBA star to a serious rap deal, this according to his agent.
Lillard's already established himself as one of the best (if not THE best) rapper in the NBA -- and famously started the 4-bar Friday freestyle rap challenge on social media.
He's also racked up more than 4.5 million plays on his SoundCloud page.
Now, the record labels want a piece of the action -- with his agent Aaron Goodwin telling TMZ Sports they've approached by "several major labels" .